Predictive modeling of relative permeability using a generalized equation of state

Prakash Purswani, Russell T. Johns, Zuleima T. Karpyn, Martin Blunt

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Reliable simulation of enhanced oil recovery (EOR) processes depends on an accurate description of fluid transport in the subsurface. Current empirical transport models of rock-fluid interactions are fit to limited experimental data for specific rock types, fluids, and boundary conditions. In this paper, a general equation-of-state (EoS) approach is developed for relative permeability (kr) based on a set of geometric state parameters: normalized Euler characteristic (connectivity) and saturation. Literature data and pore network modeling (PNM) simulations are used to examine the functional form of the EoS. Our results show that the new kr-EoS matches experimental data better than the conventional Corey form, especially for highly nonlinear relative permeabilities at low saturations. Using hundreds of PNM simulations, relative permeability scanning curves show a locus of residual saturation and connectivity that defines an important limit for the physical kr region. The change of this locus is also considered for two contact angles. PNM data further allow for the estimation of the relative permeability partial derivatives that are used as inputs in the EoS. Linear functions of these partials in the connectivity-saturation space renders a quadratic response of kr, which shows excellent predictions. Unlike current empirical models that are based on only one residual saturation, the state function approach allows for dynamic residual conditions critical for capturing hysteresis in relative permeability.

Original languageEnglish (US)
Pages (from-to)191-205
Number of pages15
JournalSPE Journal
Issue number1
StatePublished - Feb 2021

All Science Journal Classification (ASJC) codes

  • Energy Engineering and Power Technology
  • Geotechnical Engineering and Engineering Geology


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